Question

solve the following quadratic equations by completing the square method 2y square + 9y + 10 =0

Answer 1

Solution :

2y² + 9y + 10 = 0

=> 2y² + 9y = -10

Divide each term by 2 , we get

=> y² + 9y/2 = -5

=> y² + 2 × y × ( 9/4 ) = -5

=> y² + 2× y × ( 9/4) + ( 9/4 )² = -5 + (9/4)²

=> ( y + 9/4 )² = -5 + 81/16

=> ( y + 9/4 )² = ( -80 + 81 )/16

=> ( y + 9/4 )² = 1/4²

=> y + 9/4 = ± 1/4

=> y = -9/4 ± 1/4

=> y = ( -9 ± 1 )/4

=> y = ( -9 + 1 )/4 or y = ( -9 - 1 )/4

=> y = -8/4 or y = -10/4

=> y = -2 or y = -5/2

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